\subsection*{实验3.最小偏向角法测量棱镜的折射率}
\subsubsection*{(1)原始数据记录表格}


\begin{center}
\begin{tabular}{|c|c|c|c|c|c|c|}
\hline 
\multicolumn{2}{|c|}{次数} & 1 & 2 & 3 & 4 & 5 \\ 
\hline 
\multirow{2}{*}{\text{入射角}}
& ${\alpha}_1$ 
{% for a in ANGLE_A1_MIN %}
& %% a.angle %%$^{\circ}$%% a.minus %%'
{%- endfor %}
\\  
\cline{2-7}
& ${\beta}_1$ 
{% for a in ANGLE_B1_MIN %}
& %% a.angle %%$^{\circ}$%% a.minus %%'
{%- endfor %}
\\ 
\hline 
\multirow{2}{*}{\text{折射角}}
& ${\alpha}_2$ 
{% for a in ANGLE_A2_MIN %}
& %% a.angle %%$^{\circ}$%% a.minus %%'
{%- endfor %} 
\\ 
\cline{2-7}
& ${\beta}_2$ 
{% for a in ANGLE_B2_MIN %}
& %% a.angle %%$^{\circ}$%% a.minus %%'
{%- endfor %} 
\\ 
\hline 
\multicolumn{2}{|c|}{${\delta}_{min}$} 
{% for a in ANGLE_DELTA_MIN %}
& %% a.angle %%$^{\circ}$%% a.minus %%'
{%- endfor %}\\ 
\hline 
\end{tabular} 
\end{center}
\vspace{10pt}

\begin{center}
${\delta}_{min}$是最小偏向角，且有${\delta}_{min}$ = $\displaystyle\frac{1}{2}[({\alpha}_2-{\alpha_1})+({\beta}_2-{\beta}_1)]$
\end{center}

${\delta}_{min}$的平均值为：$$\bar{{\delta}_{min}}=\displaystyle\frac{1}{5}\sum\limits_{i=1}^{5}{{\delta}_{min}}=%% AVERAGE_MIN %%rad$$

$$ n_1=\displaystyle\frac{\sin{\displaystyle\frac{{\delta}_{min}+A}{2}}}{\sin{\displaystyle\frac{A}{2}}} = \displaystyle\frac{\sin{\displaystyle\frac{ %% AVERAGE_A %% + %% AVERAGE_MIN %% }{2}}}{\sin{\displaystyle\frac{ %% AVERAGE_A %% }{2}}} = %% N1 %% $$

\subsubsection*{(2)不确定度的计算}
${\delta}_{min}$的A类不确定度：
$$u_a({\delta}_{min}) = \sqrt{\displaystyle\frac{\sum\limits_{i=1}^{5}({\delta}_{min}-\bar{{\delta}_{min}})}{5{\times}(5-1)}^2 } = %% UA_MIN %% $$

${\delta}_{min}$的B类不确定度：
$$u_b({\delta}_{min})=\displaystyle\frac{\bigtriangleup\text{仪}}{\sqrt{3}}
= \frac{1'}{\sqrt{3}} = \frac{\pi}{180\times60\times\sqrt{3}} = 1.6794 \times 10^{-4} $$

${\delta}_{min}$的不确定度：
$$u({\delta}_{min}) = \sqrt{u^2_a({\delta}_{min})+u^2_b({\delta}_{min})} = %% U_MIN %%$$

$$u(A) = %% U_A %% $$

$$u(n_1) = \sqrt{(\displaystyle\frac{{\partial}n_1}{{\partial}{\delta}_{min}})^2{\times}u^2({\delta}_{min})+(\displaystyle\frac{{\partial}n_1}{{\partial}A})^2u^2(A)} = %% U_N1 %% $$

相对不确定度：
$$\displaystyle\frac{u(n_1)}{n_1} = %% RE_U_MIN %%$$

最终结果:
$${n_1}{\pm}u({n_1}) = %% RESULT_N1 %% {\pm} %% RESULT_U_N1 %% $$